Hemispherical shell resonator(HSR)is the core component of hemispherical resonator gyro.It is aφ-shaped small-bore complex component with minimum curvature radius less than 3 mm.Thus,traditional polishing methods are...Hemispherical shell resonator(HSR)is the core component of hemispherical resonator gyro.It is aφ-shaped small-bore complex component with minimum curvature radius less than 3 mm.Thus,traditional polishing methods are difficult to polish it.Small ball-end magnetorheological polishing method can polish the small components with complicated three-dimensional surface and obtain non-destructive surface.Therefore,this method is suitable for polishing HSR.However,the material removal rate of the ordinary small ball-end magnetorheological polishing is low,leading to long polishing time and low output of HSR.To solve this problem,a water bath heating assisted small ball-end magnetorheological polishing method is proposed in this research.The influence rule of processing parameters on the material removal rate is studied experimentally.A set of optimal processing parameters is obtained to maximize the material removal rate.Compared with the ordinary method,the material removal rate of the new method can be improved by 143%.Subsequently,an HSR is polished by the new method.The results show that the polishing time can be reduced by 55%,and the polished surface roughness can reach 7.7 nm.The new method has the great potential to be used in actual production to improve the polishing efficiency of HSR.展开更多
We obtain new upper tail probabilities of m-times integrated Brownian motions under the uniform norm and the Lp norm. For the uniform norm, Talagrand's approach is used, while for the Lp norm, Zolotare's appro...We obtain new upper tail probabilities of m-times integrated Brownian motions under the uniform norm and the Lp norm. For the uniform norm, Talagrand's approach is used, while for the Lp norm, Zolotare's approach together with suitable metric entropy and the associated small ball probabilities are used. This proposed method leads to an interesting and concrete connection between small ball probabilities and upper tail probabilities(large ball probabilities) for general Gaussian random variables in Banach spaces. As applications,explicit bounds are given for the largest eigenvalue of the covariance operator, and appropriate limiting behaviors of the Laplace transforms of m-times integrated Brownian motions are presented as well.展开更多
Using the theory of small ball estimate to study the biological population for keeping ecological balance in an ecosystem, we consider a Brownian motion with variable dimen- sion starting at an interior point of a gen...Using the theory of small ball estimate to study the biological population for keeping ecological balance in an ecosystem, we consider a Brownian motion with variable dimen- sion starting at an interior point of a general parabolic domain Dt in Rd（t）＋1 where d（t） ≥ 1 is an increasing integral function as t →∞, d（t） →∞. Let TOt denote the first time the Brownian motion exits from Dr. Upper and lower bounds with exact constants of log P（rDt 〉 t） are given as t →∞, depending on the shape of the domain Dr. The problem is motivated by the early results of Lifshits and Shi, Li, Lu in the exit proba- bilities. The methods of proof are based on the calculus of variations and early works of Lifshits and Shi, Li, Shao in the exit probabilities of Brownian motion.展开更多
Let {Xm（t）, t∈R＋} be an m-Fold integrated Brownian motion. In this paper, with the help of small ball probability estimate, a functional law of the iterated logarithm （LIL） for Xm（t） is established. This exten...Let {Xm（t）, t∈R＋} be an m-Fold integrated Brownian motion. In this paper, with the help of small ball probability estimate, a functional law of the iterated logarithm （LIL） for Xm（t） is established. This extends the classic Chung type liminf result for this process. Furthermore, a result about the weighted occupation measure for Xm（t） is also obtained.展开更多
基金supported by the National Key Research and Development Program of China(No.2022YFB3403600)the National Natural Science Foundation of China(No.52293403)Self-Planned Task of State Key Laboratory of Robotics and System(HIT)(No.SKLRS202204C)。
文摘Hemispherical shell resonator(HSR)is the core component of hemispherical resonator gyro.It is aφ-shaped small-bore complex component with minimum curvature radius less than 3 mm.Thus,traditional polishing methods are difficult to polish it.Small ball-end magnetorheological polishing method can polish the small components with complicated three-dimensional surface and obtain non-destructive surface.Therefore,this method is suitable for polishing HSR.However,the material removal rate of the ordinary small ball-end magnetorheological polishing is low,leading to long polishing time and low output of HSR.To solve this problem,a water bath heating assisted small ball-end magnetorheological polishing method is proposed in this research.The influence rule of processing parameters on the material removal rate is studied experimentally.A set of optimal processing parameters is obtained to maximize the material removal rate.Compared with the ordinary method,the material removal rate of the new method can be improved by 143%.Subsequently,an HSR is polished by the new method.The results show that the polishing time can be reduced by 55%,and the polished surface roughness can reach 7.7 nm.The new method has the great potential to be used in actual production to improve the polishing efficiency of HSR.
基金supported by the Simons Foundation(Grant No.246211)
文摘We obtain new upper tail probabilities of m-times integrated Brownian motions under the uniform norm and the Lp norm. For the uniform norm, Talagrand's approach is used, while for the Lp norm, Zolotare's approach together with suitable metric entropy and the associated small ball probabilities are used. This proposed method leads to an interesting and concrete connection between small ball probabilities and upper tail probabilities(large ball probabilities) for general Gaussian random variables in Banach spaces. As applications,explicit bounds are given for the largest eigenvalue of the covariance operator, and appropriate limiting behaviors of the Laplace transforms of m-times integrated Brownian motions are presented as well.
文摘Using the theory of small ball estimate to study the biological population for keeping ecological balance in an ecosystem, we consider a Brownian motion with variable dimen- sion starting at an interior point of a general parabolic domain Dt in Rd（t）＋1 where d（t） ≥ 1 is an increasing integral function as t →∞, d（t） →∞. Let TOt denote the first time the Brownian motion exits from Dr. Upper and lower bounds with exact constants of log P（rDt 〉 t） are given as t →∞, depending on the shape of the domain Dr. The problem is motivated by the early results of Lifshits and Shi, Li, Lu in the exit proba- bilities. The methods of proof are based on the calculus of variations and early works of Lifshits and Shi, Li, Shao in the exit probabilities of Brownian motion.
基金Supported by Funding from the Department of Radiology,Marmara University School of Medicine
文摘AIM: To highlight magnetic resonance enterography (MRE) for diagnosis of patients with refractory iron deficiency anemia and normal endoscopy results.
基金Project supported by the National Natural Science Foundation of China (No.10131040)the Specialized Research Fund for the Doctor Program of Higher Education (No.2002335090).
文摘Let {Xm（t）, t∈R＋} be an m-Fold integrated Brownian motion. In this paper, with the help of small ball probability estimate, a functional law of the iterated logarithm （LIL） for Xm（t） is established. This extends the classic Chung type liminf result for this process. Furthermore, a result about the weighted occupation measure for Xm（t） is also obtained.
